Composite Functions

Last updated about 3 years ago

5 questions

In evaluating function compositions, we substituted the value of x into the input function, then used the output from that function as the input on the next function. 

Given 𝑓(𝑥) = 3𝑥 +1 and 𝑔(𝑥) = 2𝑥+3, find

a. f(g(x))

b. g(f(x))

c. f(f(x))

Given 𝑓(𝑥) = 𝑥2+1 and 𝑔(𝑥) = 𝑥+3, find

a. f(g(x))

b. g(f(x))

c. g(g(x))

Board of Fame question:

A store offers a 15% discount on all items and you also have a $10 coupon. Both discounts can be applied to your purchase. Write a function rule, 𝑓(𝑥) for using the coupon and a function rule, 𝑔(𝑥) for using the 15% discount.

a. Write a function composition rule for using the $10 coupon first and then taking the 15% discount and another rule for using the 15% discount first and then taking the $10 coupon.

b. Which will give the lowest purchase cost?

Composite Functions

Composite Functions

Given 𝑓(𝑥) = 3𝑥 +1 and 𝑔(𝑥) = 2𝑥+3, find

a. f(g(x))

b. g(f(x))

c. f(f(x))

Given 𝑓(𝑥) = 𝑥2+1 and 𝑔(𝑥) = 𝑥+3, find

a. f(g(x))

b. g(f(x))

c. g(g(x))

Homework:

Homework:

Given 𝑓(𝑥) = 3𝑥 +1 and 𝑔(𝑥) = 2𝑥+3, find

a. f(g(x))

b. g(f(x))

c. f(f(x))

Given 𝑓(𝑥) = 𝑥2+1 and 𝑔(𝑥) = 𝑥+3, find

a. f(g(x))

b. g(f(x))

c. g(g(x))

Homework:

Homework:

Composite Functions

Composite Functions

Given 𝑓(𝑥) = 3𝑥 +1 and 𝑔(𝑥) = 2𝑥+3, find a. f(g(x))b. g(f(x))c. f(f(x))

Given 𝑓(𝑥) = 𝑥2+1 and 𝑔(𝑥) = 𝑥+3, find a. f(g(x))b. g(f(x))c. g(g(x))

Homework:

Homework:

Given 𝑓(𝑥) = 3𝑥 +1 and 𝑔(𝑥) = 2𝑥+3, find a. f(g(x))b. g(f(x))c. f(f(x))

Given 𝑓(𝑥) = 𝑥2+1 and 𝑔(𝑥) = 𝑥+3, find a. f(g(x))b. g(f(x))c. g(g(x))

Homework:

Homework:

Given 𝑓(𝑥) = 3𝑥 +1 and 𝑔(𝑥) = 2𝑥+3, find

a. f(g(x))

b. g(f(x))

c. f(f(x))

Given 𝑓(𝑥) = 𝑥2+1 and 𝑔(𝑥) = 𝑥+3, find

a. f(g(x))

b. g(f(x))

c. g(g(x))

Given 𝑓(𝑥) = 3𝑥 +1 and 𝑔(𝑥) = 2𝑥+3, find

a. f(g(x))

b. g(f(x))

c. f(f(x))

Given 𝑓(𝑥) = 𝑥2+1 and 𝑔(𝑥) = 𝑥+3, find

a. f(g(x))

b. g(f(x))

c. g(g(x))